subring

1 9.9

A set inside a ring that stays the same when you add or multiply its elements

noun
/ˈsʌbˌrɪŋ/

Specialized

: subanillo

Then the intersection is a subring, and if those subrings are a chain under inclusion, then the union is also a subring.

Examples

In algebra, a subring of the integers includes all even numbers, as it satisfies ring properties.
To verify that a set forms a subring, you must check that it is closed under addition and multiplication.
Every ideal in a ring is also a subring, since it contains the necessary structure to be considered one.

Surface Forms

subring singular

subrings plural

Morphology

subring = ring (transparent) = sub + ring

Formed by the productive prefix 'sub-' meaning 'under/secondary' plus 'ring'; in mathematics it directly denotes a ring contained within another ring.

Etymology

The word subring has two parts: sub- meaning 'under' as in subway, and ring, which you can think of as a circle or a small group. So a subring is a smaller 'ring' inside a larger ring in math, a smaller set that still uses the same operations.